A PD code yields two different knot diagrams

sophiatev
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The same PD code seems to yield two different knot diagrams of the Hopf link
The PD code [(2, 3, 1, 4), (4, 1, 3, 2)] seems to map to a non-unique knot diagram. I can describe the following two Hopf links with different orientations with this same PD code. As I understand it, while a link diagram does not have a unique PD code, a given PD code should map to just one knot diagram. Am I missing something?

IMG-6314.jpg
 
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Sorry, the PD code maps to a unique *link* diagram, so the Hopf link is a valid diagram (also, a ring is the unknot so it's still a knot, right? The Hopf link is just two linked unknots)
 
I don't know if it helps, but:

Make half a turn (the least complicated direction) of one of the 4 rings around the horizontal axis.
 
A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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